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4 years ago

2 math questions. :)

Mathematics

2 answers:

Katen [24]4 years ago

6 0

4.
GH = EF (third choice)

5.
GH = EH (second choice)

timama [110]4 years ago

5 0

5. is EH

Look for a side across from it that is similar

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The sum of 4 times a number and 7 equals 2 Use the variable y for the unknown number.

nataly862011 [7]

Answer:

4y + 7 = 2

Step-by-step explanation:

7 0

3 years ago

Can someone please help me with this question.

Ber [7]

Answer:

square root of 2

Step-by-step explanation:

Sides are 1 and 1 and the hypotenuse is the longest side (opposite the right angle)

We can use pythagerouses theorem : a^2+b^2=c^2

this means that 1^2+1^2=c^2

1+1=c^2

2=c^2

c=2/sqrt

c is the square root of 2

the hypotenuse is the square root of 2

4 0

3 years ago

g Z-Test for Population Means Calculate z-statistic of a population mean. Keith sampled 10 private universities in Colorado and

scoray [572]

Answer: 2.46

Step-by-step explanation:

Formula for x-score is given by :-

$Z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

, where $\overline{x}$ = Sample mean , $\mu$ = population mean, $\sigma$ = population standard deviation, n= sample size.

As per given , n=10

$\mu$ = $29,056

$\sigma$ = $3,339

$\overline{x}$ = $31,650

Then,

$z=\dfrac{ 31650-29056}{\dfrac{3339}{\sqrt{10}}}\\\\=\dfrac{2594}{\dfrac{3339}{3.16227766017}}\\\\=\dfrac{2594}{1055.88451073}=2.45670807142\approx 2.46$

Hence, the z-score = 2.46

4 0

3 years ago

Last month, 349 books were checked out from the school library. This month, 273 books were checked out. Find the Percent of Chan

Alexeev081 [22]

Last month to this month

8 0

3 years ago

Identify the standard form of the equation by completing the square.

OLEGan [10]

Answer:

$\dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1$

Step-by-step explanation:

Given equation:

$4x^2-9y^2-8x+36y-68=0$

This is an equation for a horizontal hyperbola.

To complete the square for a hyperbola

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side.

$\implies 4x^2-8x-9y^2+36y=68$

Factor out the coefficient of the x² term and the y² term.

$\implies 4(x^2-2x)-9(y^2-4y)=68$

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

$\implies 4\left(x^2-2x+\left(\dfrac{-2}{2}\right)^2\right)-9\left(y^2-4y+\left(\dfrac{-4}{2}\right)^2\right)=68+4\left(\dfrac{-2}{2}\right)^2-9\left(\dfrac{-4}{2}\right)^2$

$\implies 4\left(x^2-2x+1\right)-9\left(y^2-4y+4\right)=36$

Factor the two perfect trinomials on the left side:

$\implies 4(x-1)^2-9(y-2)^2=36$

Divide both sides by the number of the right side so the right side equals 1:

$\implies \dfrac{4(x-1)^2}{36}-\dfrac{9(y-2)^2}{36}=\dfrac{36}{36}$

Simplify:

$\implies \dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1$

Therefore, this is the standard equation for a horizontal hyperbola with:

center = (1, 2)
vertices = (-2, 2) and (4, 2)
co-vertices = (1, 0) and (1, 4)
$\textsf{Asymptotes}: \quad y = -\dfrac{2}{3}x+\dfrac{8}{3} \textsf{ and }y=\dfrac{2}{3}x+\dfrac{4}{3}$
$\textsf{Foci}: \quad (1-\sqrt{13}, 2) \textsf{ and }(1+\sqrt{13}, 2)$

4 0

2 years ago